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Statement-1 A toroid produces uniform ma...

Statement-1 A toroid produces uniform magnetic field.
Statement-2 A toroid is a simple solenoid bent into the shape of a hoop, so it is like an endless solendoid.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-4

B

Statement-1 is True, Statement-2, is True, Statement-2 is NOT a correct explanation for Statement-4

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given statements, we will evaluate each statement and determine their validity. ### Step 1: Understanding Statement 1 **Statement 1:** A toroid produces a uniform magnetic field. - A toroid is a doughnut-shaped coil of wire. When an electric current passes through it, a magnetic field is generated inside the toroid. - The magnetic field inside a toroid can be expressed by the formula: \[ B = \frac{\mu_0 n I}{2 \pi r} \] where: - \( B \) is the magnetic field, - \( \mu_0 \) is the permeability of free space, - \( n \) is the number of turns per unit length, - \( I \) is the current flowing through the wire, - \( r \) is the distance from the center of the toroid to the point where the magnetic field is being measured. - Inside the toroid, the magnetic field is uniform at any point equidistant from the center, as it depends only on the current and the number of turns, not on the position along the circular path. **Conclusion for Statement 1:** True. ### Step 2: Understanding Statement 2 **Statement 2:** A toroid is a simple solenoid bent into the shape of a hoop, so it is like an endless solenoid. - A solenoid is a long coil of wire that produces a magnetic field when current flows through it. The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid. - When a solenoid is bent into a circular shape, it forms a toroid. The ends of the solenoid connect to form a continuous loop, which is why it can be considered as an "endless" solenoid. - The magnetic field inside a toroid behaves similarly to that of a long solenoid, as the magnetic field lines are concentrated within the loop and are uniform. **Conclusion for Statement 2:** True. ### Step 3: Relationship Between the Statements - Since both statements are true and Statement 2 provides a correct explanation for Statement 1, we can conclude that both statements are valid. ### Final Conclusion Both Statement 1 and Statement 2 are true, and Statement 2 is a correct explanation for Statement 1. ---
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